Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#131 ⋊ C2 |
| Sylow | C7 ⋊ #443 |
106 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,11,12,14,13,19,22,23)(9,15,16,21,18,10,17,20);(8,10)(9,14)(11,17)(12,20)(13,15)(16,19)(18,23)(21,22);(2,3)(4,5)(6,7)(8,9)(10,19)(11,15)(12,16)(13,18)(14,21)(17,22)(20,23)Polycyclic presentation:
2^6,7|c^2=d,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^6,e^b=ef88 conjugacy classes — view the full character table.
| maximal subgroup of | #11726876, #11726877, #11729206, … |
| maximal normal subgroup of | #11726876, #11726877, #11729206, … |
| maximal quotient of | #11727641, #11727643, #11727653, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 678);